Question: Solve for $x$ and $y$ using elimination. $\begin{align*}8x+4y &= 8 \\ -3x-4y &= 1\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $5x = 9$ Divide both sides by $5$ and reduce as necessary. $x = \dfrac{9}{5}$ Substitute $\dfrac{9}{5}$ for $x$ in the top equation. $8( \dfrac{9}{5})+4y = 8$ $\dfrac{72}{5}+4y = 8$ $4y = -\dfrac{32}{5}$ $y = -\dfrac{8}{5}$ The solution is $\enspace x = \dfrac{9}{5}, \enspace y = -\dfrac{8}{5}$.